Detecting changes in autoregressive processes with (X)over-bar and EWMA charts

The traditional use of control charts necessarily assumes the independence of data. It is now recognized that many processes are autocorrelated thus v iolating the fundamental assumption of independence. As a result, there is a need for a broader approach to SPC when data are time-dependent or autoco rrelated. This paper utilizes control charts with fixed control limits for residuals to monitor the performance of a process yielding time-dependent d ata subject to shifts in the mean and the autocorrelation structure. The ef fectiveness of the framework is evaluated by an average run length study of both Xmacr and EWMA charts using analytical and simulation techniques. Ave rage run lengths are tabulated for various process disturbance scenarios, a nd recommendations for the most effective monitoring tool are made. The fin dings of this research present motivation to extend the traditional paradig ms of a shifted process (e.g., mean and/or variance). The results show that decreases in the underlying time series parameters are practically impossi ble to detect with standard control charts. Furthermore, the practitioner i s motivated to employ runs rules since the runs are more likely with time-d ependent observations.